Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditioned matrix. Comparison theorems show that the rate of convergence of the preconditioned Gauss-Seidel method is faster than the preconditioned mixed-type splitting and AOR (SOR) iterative methods. Finally, some numerical examples are presented to illustrate the reality of our comparison theorems.
Mohseni Moghadam, M. & Panjeh Ali Beik, F. (2012). Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems. Bulletin of the Iranian Mathematical Society, 38(2), 349–367.
MLA
Mohseni Moghadam, M., & Panjeh Ali Beik, F. "Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems", Bulletin of the Iranian Mathematical Society, 38, 2, 2012, 349–367.
HARVARD
Mohseni Moghadam, M., & Panjeh Ali Beik, F. (2012). 'Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems', Bulletin of the Iranian Mathematical Society, 38(2), pp. 349–367.
CHICAGO
Mohseni Moghadam, M. & Panjeh Ali Beik, F., "Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems." Bulletin of the Iranian Mathematical Society, 38 2 (2012): 349–367,
VANCOUVER
Mohseni Moghadam M., Panjeh Ali Beik F. Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems. BIMS. 2012;38(2):349–367.
